but appearances, mere phenomena. Space and time do not
belong to things as they are in themselves, but rather to
our way of looking at things. They are forms of our per-
ception. It is our minds which impose space and time upon
objects, and not objects which impose space and time upon
our minds. Further, Kant drew from these contradictions
the conclusion that to comprehend the infinite is beyond
the capacity of human reason. He attempted to show that,
wherever we try to think the infinite, whether the infinitely
large or the infinitely small, we fall into irreconcilable con-
tradictions. Therefore, he concluded that human faculties
are incapable of apprehending infinity. As might be ex-
pected, many thinkers have attempted to solve the problem
by denying one or other side of the contradiction, by saying
that one or other side does not follow from the premises,
that one is true and the other false. David Hume, for exam-
ple, {58} denied the infinite divisibility of space and time,
and declared that they are composed of indivisible units
having magnitude. But the difficulty that it is impossi-
ble to conceive of units having magnitude which are yet
indivisible is not satisfactorily explained by Hume. And
in general, it seems that any solution which is to be sat-
isfactory must somehow make room for both sides of the
contradiction. It will not do to deny one side or the other,
to say that one is false and the other true. A true solution
is only possible by rising above the level of the two antago-
nistic principles and taking them both up to the level of a
higher conception, in which both opposites are reconciled.
This was the procedure followed by Hegel in his solution of
the problem. Unfortunately his solution cannot be fully un-
derstood without some knowledge of his general philosoph-
ical principles, on which it wholly depends. I will, however,
try to make it as plain as possible. In the first place, Hegel
did not go out of his way to solve these antinomies. They
appear as mere incidents in the development of his thought.
He did not regard them as isolated cases of contradiction
which occur in thought, as exceptions to a general rule,
which therefore need special explanation. On the contrary,
he regarded them, not as exceptions to, but as examples
of, the essential character of reason. All thought, all rea-
son, for Hegel, contains immanent contradictions which it
first posits and then reconciles in a higher unity, and this
particular contradiction of infinite divisibility is reconciled
in the higher notion of quantity. The notion of quantity
contains two factors, namely the one and the many. Quan-
tity means precisely a many in {59} one, or a one in many.
If, for example, we consider a quantity of anything, say a
heap of wheat, this is, in the first place, one; it is one whole.
Secondly, it is many; for it is composed of many parts. As
one it is continuous; as many it is discrete. Now the true
notion of quantity is not one, apart from many, nor many
apart from one. It is the synthesis of both. It is a manyin
one. The antinomy we are considering arises from consid-
ering one side of the truth in a false abstraction from the
other. To conceive unity as not being in itself multiplicity,
or multiplicity as not being unity, is a false abstraction.
The thought of the one involves the thought of the many,
and the thought of the many involves the thought of the
one. You cannot have a many without a one, any more than
you can have one end of a stick without the other. Now,
if we consider anything which is quantitatively measured,